I like to start with the ressources of Sol revealed, but if you do not, build a geosurvey ship first. It doesn't have to be fancy, it is only for Sol.
For that you need an engine, hopefully you have at least the first engines, better yet if you already have ion engines. Use a civilian one here (size 25 and up, 50% Power or less, iirc), they use less fuel and civilian designs don't need regular maintenance. I prefer to build civ engines as large as possible, size 50.
You can build the ship(s) with the ressource points you had at the beginning, no need to tool a shipyard for that yet.
Explore Luna, Mars, and then autoexplore (special orders tab, default orders: survey next 5 system bodies. Set conditional orders to refuel at 20%. When you leave Sol later set that higher (depending on you tanks, of course) so your ships don't run out of fuel on the way back.)
Then you should decide where to put your first colony, Mars or Luna. Use the one with better ressources, if any are to be had, if not use Mars, it is easier to terraform.
Build some infrastructure on earth, about 1000 should be enough, and a freighter and a colony ship. Use the same engines you already have if you built the geosurvey ship. Use the points you have left for those, these ships will be obsolete fairly soon anyway.
Ferry the infrastructure to the desired location (you can tick the repeat orders box, so it will do so until there is nothing left on earth), then ferry some colonists. Fairly soon the civvie shipping line should build a ship. Hopefully it is a freighter, so they will bring more infractructure to your colony, and you don't even have to produce it yourself.
In the meantime, research whatever you like, though better engines are the most important thing right now. If you don't have a specialized researcher use the one with the biggest bonus. Better engine/reactor tech and less fuel consumption are the main targets.
I generally set 15% of my production capacity to produce mines, another 15% to produce more factories. The remaining 70% is used for what I need. That is mainly more labs, maybe added factories to kickstart production, a shipyard or three, depending on what you started with, more academies to get that engine specialist, a sector command once you have improved command and control researched (logistics/ground combat). Later automines are important, but you can ship those that are already on earth somewhere else first.
Assign your highest officer to fleet command, tick the automated assignements box. You can still put people on posts manually, but it takes care of all the ships and ground units you don't want to manually assign officers to.
It only works for the military and your civilan shipping, so you need to assign admins to your colonies yourself.
Then build a grav survey, explore the survey points (can be automated as well) and leave Sol for the rest of the universe.
All this only works if you already start with trans-newtonian tech, otherwise you'll be on earth for a long time researching the necessary stuff. I would not recommend that for beginners.
If you just want to learn the ropes you can disable NPRs and AI opponents, but I would leave the precursors in, because they can teach you combat, but they won't come after you and attack earth.
Something I like to do as well is increase the tolerance for humans, so they can settle more planets, because I want an empire, not 3 barely habitable planets between 10 sectors.
I haven't played in a while, so I probably forgot something.
